The Chilean has said recently that his future is in the hands of his agent as contract negotiations continue to stall with Arsenal.
"The club have got to make it an issue now and give the players the wages they want," said Parlour via The Independent.
"They have got to step up now. I would say to Sanchez, 'how much do you want?'
"If his agent says, 'we want £300,000-a-week' you have to pay it I'm afraid.
"They have come fifth in the league this year, which we know is not good enough for Arsenal's standards. They won a trophy in the FA Cup."